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Trigonometric Derivatives

The derivatives of trig functions follow beautiful patterns. Memorize these - you'll use them constantly!

Trig Derivatives
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Memory Trick

Notice: co-functions get negative signs!
- sin → cos (no negative)
- cos → -sin (negative)
- tan → sec^2 (no negative)
- cot → -csc^2 (negative)

Trig Derivative with Chain Rule
Easy
Find d/dx[sin(3x)]
1
Apply chain rule
d/dx[sin(3x)] = cos(3x) * 3 = 3cos(3x)
Answer: 3cos(3x)

Practice

1. d/dx[cos(2x)] = ?
sin(2x)
-sin(2x)
-2sin(2x)
2sin(2x)
2. d/dx[tan(x^2)] = ?
sec^2(x^2)
2xsec^2(x^2)
2xtan(x^2)
sec^2(2x)
Key Takeaways

  • sin → cos, cos → -sin

  • tan → sec^2, cot → -csc^2

  • Co-functions get negative signs

  • Always apply chain rule when there's a composite!